A389276 a(n) = Sum_{i=1..n} (Product_{j=1..n} M(j, ((i+j-2) mod n)+1) + Product_{j=1..n} M(j, ((i-j-1) mod n)+1)) where M is the n X n matrix with numbers 1, 2, ..., n^2 in order across rows.

0, 2, 20, 450, 18528, 1214850, 116086464, 15216643750, 2618940881920, 572574715514406, 154951850455584000, 50837568234198964218, 19878132914699412326400, 9131977150353330603980650, 4869531091223985264201281536, 2982755204766415743731748708750, 2079817858335583811095557003804672

Offset

0,2

Comments

It differs from A389261 in the sign between the two products.

Links

Table of n, a(n) for n=0..16.

Example

a(1) = 1 + 1 = 2:
  [1]
a(2) = 1*4 + 2*3 + 2*3 + 1*4 = 20:
  [1, 2]
  [3, 4]
a(3) = A232773(3) = 1*5*9 + 2*6*7 + 3*4*8 + 3*5*7 + 1*6*8 + 2*4*9 = 450:
  [1, 2, 3]
  [4, 5, 6]
  [7, 8, 9]
a(6) = 116086464:
  [ 1,  2,  3,  4,  5,  6]
  [ 7,  8,  9, 10, 11, 12]
  [13, 14, 15, 16, 17, 18]
  [19, 20, 21, 22, 23, 24]
  [25, 26, 27, 28, 29, 30]
  [31, 32, 33, 34, 35, 36]

Mathematica

M[i_, j_, n_]:=j+(i-1)n; a[n_]:=Sum[Product[M[j, Mod[i+j-2, n]+1, n], {j, n}]+Product[M[j, Mod[i-j-1, n]+1, n], {j, n}], {i, n}]; Array[a, 17, 0]

Crossrefs

Cf. A232773, A389261.

Sequence in context: A012533 A009160 A188811 * A009252 A210901 A274572

Adjacent sequences: A389273 A389274 A389275 * A389277 A389278 A389279

Keyword

nonn

Author

Stefano Spezia, Sep 28 2025

Status

approved